Hi, I have the following dynamical system,

x_{n+1}={x_n}^2-{y_n}^2+a
y_{n+1}=2x_ny_n

Where a is real.

And I am asked to consider the set of points on a circle of radius r and centre origin and show that they are mapped to another circle under one iteration.

How do I go about this? I know the equation for the circle is of course x^2+y^2 = r^2. Can someone please give me a clue how to start?

Thanks,
Katy